1. Field of the Invention
The present invention relates generally to steam turbine blades and, more specifically, to a freestanding mixed tuned blade designed as a retrofit into an existing turbine rotor.
2. Description of the Related Art
Steam turbines include several rows of rotating and staitonary blades. The stationary blades are mounted on the stationary cylinder which surrounds the turbine rotor, whereas rotating blades are mounted in rows on the rotor and thus rotate with the rotor.
The blades of any given row are usually ientical. Most blades include a root portion which is used to mount the blade in its corresponding mounting structure, a platform portion, and an airfoil portion.
One known type of root portion is designed to be fitted into a side-entry groove of the rotor. The overall configuration of the groove is arcuately shaped and thus the root portion for a side-entry blade is also generally arcuately shaped. Within the category of side-entry blades, one type of root configuration is known as the "fir tree", due to the fact that the shape of the root portion is somewhat like an inverted fir tree. In this type of root portion, there are a series of alternating necks and lugs which interfit with correspondign necks and lugs provided in the rotor groove.
The design of a root portion is an exacting science, one in which slight changes in the configuration of a neck or lug can result in substantial changes in the stress distribution imposed on the entire root portion.
The design of the airfoil portion of the blade is also extremely difficult. The airfoil portions of most steam turbine rotor blades include a leading edge, a trailing edge, a concave pressure-side surface, a convex suction-side surface, and a tip at the distal end opposite the root portion. The airfoil portion shape common to a particularly row of rotor blades differs from the airfoil portion shaped for every other row within a particular turbine. Likewise, no two turbines of different designs share airfoil portions of the same shape. The structural differences in airfoil portion shape result in significant variations in aerodynamic characteristics, stress patterns, operating temperature, and natural frequency of the airfoil portion.
Development of a turbine airfoil portion or "airfoil" for a new commercial, power generation steam turbine may require several years to complete. When designing rotating blades for a new steam turbine, a profile developer is given a certain flow field with which to work. The flow field is determiend by the inlet and outlet angles (for steam passing between adjacent rotating blades of a row), gauging, and the velocity ratio, among other things. "Gauging"]is the ratio of throat to pitch; "throat" is the straight line distance between the trailing edge of one rotor blade and the vacuum-side surface of an adjacent blade, and "pitch" is the distance between the trailing edges of adjacent rotating blade.s
Flow fiel parameters are dependent on a number of factors, including the length of the rotor blades of a particular row. The length of the blade is established early in the design stages of the steam turbine and is essentially a function of the overall designed power output of the steam turbine and the power output for that particular stage or row of blades.
Another important aspect of rotating blade design is the tuning of the blades so that throughout the harmonics of running speed destructive resonant frequencies are avoided. Thus, in the process of designing and fabricating turbine rotating blades, it is critically important to tune the resonant frequencies of the blades to minimize forced or resonant vibration. The "harmonics of running speed" is best explained by example. In a typical fossil fuel powered steam turbine, the rotor rotates at 3600 revoluations per minute (rpm) or 60 cycles per second (cps). Since one cps equals one hertz (Hz), and since simple harmonic motino can be described in terms of the angular frequency of circular motion, the running speed of 60 cps produces a first harmonic of 60 Hz, a second harmonic of 120 Hz, a third harmonic of 180 Hz, a fourth harmonic of 240 Hz, etc. Blade designers typically consider frequencies up to the seventh harmonic (420 Hz). The harmonic series of frequencies occurring at intervals of 60 Hz represent the characteristic frequencies of the normal modes of vibration of an exciting force acting upon the rotating blades. If the natural frequencies of oscillation of the rotating blades coincide with the frequencies of the harmonic series, or harmonics of running speed, a destructive resonance can result in one or more of the harmonic frequencies.
Given that exciting forces can occur at a series of frequencies, a blade designer must ensure that the natural resonant frequencies of the blade do not fall on or near any of the frequencies of the harmonic series. This would be an easier task if rotating blades were susceptible to vibration in only one direction. However, a rotating blade is susceptible to vibration in potentially an infinite number of directions. Each direction of vibration will have a different corresponding natural resonant frequency. The multi-directional nature of blade vibration is referred to as the "modes of vibration". For a row of lashed rotating blades, up to at least seven different modes or directions of vibration are considered by blade designers. Each mode of vibration establishes a different natural resonant frequencies for a given rotating blade for ag iven direction.
The first mode of vibration is a tangential vibration in the rotational direction of the rotor, and is substantially influenced by the positon of the lower of two lashing wires used to interconnect groups of rotating blades. Lowering the position of the lower lashing wire tends to increase the resonant frequency for the first mode of vibration. The second mode of vibration is a tangential vibration in the axial direction of the rotor. The position of the lower lashing wire tends to have an inverse effect on the second mode frequency such that, as the lower wire is lowered to raise the frequency in the first mode, the frequency of the second mode falls. The third mode of vibration is vibration in the "X" direction such that displacement occurs in the axial direction of a wired group of blades. The third mode of vibration is highly dependent on the number of blades per group; the frequency is lowered with the addition of more blades in the grup. The fourth mode of vibration is an in-phase vibration which is highly dependent on the position of the outer-most lashing wire. Moving the outermost lashing wire downwardly lowers the frequency in the fourth mode.
For freestanding blades, the mode shape of the first two modes is the same. However, the mode shape of the third or fourth mode, while not being an "X" shape is a torsional shape instead.
Modes of vibration beyond the third or fourth mode become increasingly complex. These modes are of different mode shapes depending on many factors, too numerous to detail here.
When turning lashed rotating blades, it is important to tune the blades with respect to the first three modes of vibration. Keeping in mind the harmonic series described above for a fossil fuel power steam turbine operating at 3600 rpm, the natural resonant frequency for a rotating blade must be tuned to avoid frequencies at intervals of 60 Hz. For example, the second harmonic occurs at 120 Hz and the third harmonic occurs at 180 Hz. The standard practice is to attempt to tune the blade having a frequency falling somewhere between 120 and 180 Hz become as close as possible to the midpoint between the two harmonics, i.e., 150 Hz. It is not unusual to have a rotating blade having a natural resonant frequency which falls between the second and third harmonics for the first mode of vibration. Therefore, it is desirable to tune the blade to have a frequency at or near 150 Hz for the first mode of vibration.
Frequencies for the second and third modes of vibration are similarly tuned to be as close as possible to a midpoint between two successive harmonics. However, frequency tests are commonly run up to and beyond the seventh mode of vibration. With respect to the fourth mode of vibration, a frequency near the seventh harmonic (420 Hz) might be expected. Therefore, the outermost lashing wire should be positioned to make sure that the resonant frequency for the fourth mode of vibration is sufficiently above the seventh harmonic.
When a new steam turbine is designed, the blade designer must tune the turbine blades so that none of the resonant frequencies for any of the modes of vibration coincide with the frequencies associated with the harmonics of running speed. Sometimes, tuning requires a trade-off with turbine performance or efficiency. For example, certain design changes may have to be made to the blade to achieve a desired resonant frequency in a particular mode. This may necessitate an undesirable change elsewhere in the turbine such as a change in the velocity ratio or a change in the pitch or width of the airfoil.
Furthermore, the blade designer must avoid non-synchronous vibration, also labelled "aeroelastic instability", which includes unstalled flutter, stalled flutter, and buffeting. This phenomenon is much more prevalent in freestanding blades. To alleviate aeroelastic instability in freestanding blades, the designer mix tunes the row of blades so that the first mode of adjacent blades vibrates at slightly different frequencies.
A difficult problem arises in the situation where a pre-existing turbine is upgraded to increase its power output. This may be done by increasing the length of the blades of one or more rows, and boring out the cylinder around the row to accommodate the greater overall length. Changes to the side entry grooves provided on the rotor are nearly impossible to make, so that retrofitted blades are usually confined to employ the same root portion as its predecessor blade.
The re-design of the airfoil follows a similar process as that of the design of a new blade. Given the length of the blade and the flow field parameters, the blade designer proceeds to generate a plurality of basic blade sections. An example of a prior art blade is illustrated in FIGS. 1 through 4. Referring to FIG. 1, the basic sections are A--A through G--G. These sections compose six blade developments, the first development being from sectino A--A to B--B, the second development being from B--B to C--C, the third development being from C--C to D--D, etc. The airfoil sections of the blade are composed of the basic transverse sections through the airfoil. Each section is defined by a series of numbered coordinate points connected by a smooth continuous curve generated by spline interpolation. These coordinate points are defined according to the X--X and Y--Y axes which are illustrated in FIGS. 3 and 4. FIG. 4 shows a typical section, which happens to be the F--F section. Also, the root portion is transposed under the section to show the relationship of the root portion to the blade section. The surface between each transverse section is a ruled surface generated by a series of straight lines connecting like numbered coordinate points at each section. For example, FIG. 5 shows the tenon section (the tenon is that part of the blade which is used to attach a shroud which is used to interconnect adjacent blades in a group. The tenon section is not one of the basic sections, but is illustrated herein to show how blade design occurs. IN the attached Table I, the blade section dimensions are specified for the blade section dimensions relative to the points illustrated in FIG. 5. For example, point 1 in FIG. 5 for the tenon section si-0.320inc. (8.128 mm) in the horizontal direction (in the X direction) and -0.973 in. (24.714 mm) in the vertical direction (in the Y direction). Thus, the coordinate points for point 1 in the tenon is -0.320, -0.2973 in. (8.128, 7.551 mm).
TABLE I __________________________________________________________________________ BLADE SECTION DIMENSIONS (inches) SECTION 1 2 3 4 5 6 7 8 9 10 10A 11 __________________________________________________________________________ A-A -.450 -.353 -.257 -.160 -.063 +.034 +.130 +.227 +.324 +.420 +.475 +.517 B-B -.450 -.340 -.250 -.150 -.050 +.049 +.152 +.254 +.354 +.452 +.500 +.553 C-C -.129 -.656 -.483 -.310 -.137 +.035 +.208 +.380 +.553 +.726 +.815 +.898 D-D -1.253 -1.000 -.746 -.493 -.289 +.015 +.268 +.522 +.775 +1.029 +1.158 +1.282 E-E -1.676 -1.342 -1.008 -.673 -.339 -.005 +.329 +.663 +1.157 +1.332 +1.516 +1.666 F-F -1.976 -1.584 -1.193 -.801 -.410 -.018 +.374 +.765 +.457 +1.548 +1.757 +1.940 G-G -2.100 -1.685 -1.270 -.855 -.440 -.025 + .390 +.305 +1.220 +1.635 +1.855 +2.050 Tenon -.320 -.250 -.180 -.110 -.040 +.030 +.100 +.170 +.240 +.310 -- +.310 A-A -1.954 -1.137 -.514 +.023 +.424 +.712 +.922 +1.128 +1.308 +1.470 +1.558 +1.612 B-B -1.953 -1.205 -.667 -.155 +.265 +.605 +.870 +1.008 +1.280 +1.455 +1.540 +1.625 C-C -2.111 -1.370 -.683 -.086 +.348 +.628 +.829 +.985 +1.115 +1.230 +1.283 +1.335 D-D -2.171 -1.382 -.676 +.190 +.300 +.598 +.794 +.910 +.947 +.916 +.873 +.828 E-E -2.108 -1.292 -.333 +.031 +.400 +.641 +.752 +.744 +.635 +.439 +.296 +.173 F-F -1.953 -1.081 -.333 +.164 +.489 +.679 +.717 +.625 +.413 +.092 -.125 -.326 G-G -1.832 -.930 -.960 +.321 +.592 +.714 + .699 +.548 +.276 -.106 -.350 -.587 Tenon -.973 -.522 -.131 +.210 +.480 +.684 +.844 +.978 +1.101 +1.213 -- +1.315 __________________________________________________________________________ SECTION 12 13 14 15 16 17 18 19 20 21 21A 22 23 __________________________________________________________________________ A-A -.450 -.353 -.257 -.160 -.063 +.034 +.130 +.227 +.324 +.420 +.476 +.517 -- B-B -.450 -.340 -.250 -.150 -.050 +.049 +.152 +.254 +.354 +.452 +.500 +.553 -- C-C -.829 -.656 -.483 -.310 -.137 +.035 +.208 +.380 +.553 +.726 +.815 +.898 -- D-D -1.253 -1.000 -.746 -.493 -.239 +.015 +.268 +.522 +.775 +1.029 +1.158 +1.282 -- E-E -1.676 -1.342 -1.008 -.673 -.339 -.005 +.329 +.663 +.998 +1.332 +1.516 +1.666 -- F-F -1.976 -1.584 -1.193 -.801 -.410 -.018 +.374 +.765 +1.157 +1.548 +1.757 +1.940 -- G-G -2.100 -1.685 -1.270 -.855 -.440 -.025 +.390 +.805 +1.220 +1.548 +1.855 +2.050 -- Tenon -.320 -.250 -.180 -.110 -.040 +.030 +.100 +.170 +.240 +.310 -- +.380 -- A-A -2.105 -1.774 -1.442 -1.111 -.780 -.448 -.117 +.215 +.546 +.877 +1.109 +1.342 -1.975 B-B -2.113 -1.675 -1.308 -.903 -.512 -.131 +.225 +.543 +.825 +1.078 +1.200 +1.323 -1.974 C-C -2.213 -1.705 -1.164 -.700 -.304 +.035 +.335 +.582 +.796 +.993 +1.083 +1.172 -2.130 D-D -2.278 -1.606 -1.136 -.678 -.277 +.016 +.251 +.428 +.556 +.650 +.686 +.721 -2.195 E-E -2.199 -1.550 -1.007 -.567 - .231 +.005 +.151 +.215 +.210 +.144 +.087 +.031 -2.132 F-F -2.040 -1.347 -.814 -.425 -.163 -.013 +.043 +.018 -.082 -.254 -.373 -.492 -1.978 G-G -1.919 -1.217 -.676 -.326 -.121 -.032 -.032 -.111 -.262 -.480 -.619 -.758 -1.858 Tenon -1.622 -1.384 -1.145 -.907 -.668 -.430 -.191 +.048 +.286 +.525 -- +.763 -- __________________________________________________________________________ BLADE SECTION DIMENSIONS (millimeters) SECTION 1 2 3 4 5 6 7 8 9 10 __________________________________________________________________________ A-A -11.43 -8.966 -6.528 -4.064 -1.600 +0.864 +3.302 +5.766 +8.230 +10.668 B-B -11.43 -8.636 -6.35 -3.81 -1.27 +1.245 +3.861 +6.452 +8.992 +11.481 C-C -3.277 -16.662 -12.268 -7.874 -3.480 +0.889 +5.283 +9.652 +14.046 +18.440 D-D -31.826 -25.4 -18.948 -12.522 -7.341 +0.381 +6.807 +13.259 +19.685 +26.137 E-E -42.570 -34.087 -25.603 -17.094 -8.611 -0.127 +8.357 +16.840 +29.388 +33.833 F-F -50.190 -40.234 -30.302 -20.345 -10.414 -0.457 +9.500 +19.431 +11.608 +39.319 G-G -53.34 -42.805 -32.258 -21.717 -11.176 -0.635 +9.906 +7.74 +30.988 +41.529 Tenon -8.128 -6.35 -4.572 -2.794 -1.016 +0.762 +2.54 +4.318 +6.096 +7.874 A-A -49.632 -28.880 -13.056 +0.584 +10.770 +18.085 +23.419 +28.651 +33.223 +37.338 B-B -49.606 -30.61 -16.942 -3.937 +6.731 +15.367 +22.098 +25.603 +32.512 +36.957 C-C -53.619 -34.80 -17.348 -2.184 +8.839 +15.951 +21.057 +25.019 +28.321 +31.242 D-D -55.143 -35.103 -17.170 +4.826 +7.62 +15.189 +20.168 +23.114 +24.054 +23.266 E-E -53.543 -32.817 -8.458 +0.787 +10.16 +16.281 +19.101 +18.898 +16.129 + 11.151 F-F -49.606 -27.457 -8.458 +4.166 +12.421 +17.247 +18.212 +15.875 +10.490 +2.337 G-G -46.533 -23.622 -24.384 +8.153 +15.037 +18.136 +17.755 +13.919 +7.010 -2.692 Tenon -24.714 -13.259 -3.327 +5.334 +12.192 +17.374 +21.438 +24.841 +27.965 +30.810 __________________________________________________________________________ SECTION 10A 11 12 13 14 15 16 17 18 19 __________________________________________________________________________ A-A +12.065 +13.1318 -11.43 -8.966 -6.528 -4.064 -1.600 +0.864 +3.302 +5.766 B-B +12.7 +14.046 -11.43 -8.636 -6.35 -3.81 -1.27 +1.245 +3.861 +6.452 C-C +20.701 +22.352 -21.057 +16.662 -12.268 -7.874 -3.480 +0.889 +5.283 +9.652 D-D +29.413 +32.563 -31.826 -25.4 -18.948 -12.522 -6.071 +0.381 +6.807 +13.259 E-E +38.506 +42.316 -42.570 -34.087 -25.603 -17.094 -8.611 -0.127 +8.357 +16.840 F-F +44.628 +49.276 -50.190 -40.234 -30.302 -20.345 -10.414 -0.457 +9.500 +19.431 G-G +47.117 +52.07 -53.34 -42.799 -32.258 -21.717 -11.176 -0.635 +9.906 +20.447 Tenon -- +7.874 +8.128 -6.35 -4.572 -2.794 -1.016 +0.762 +2.54 +4.318 A-A +39.573 +40.945 -53.462 -45.060 -36.627 -28.219 -19.812 -11.379 -2.972 +5.461 B-B +39.116 +41.275 -53.670 -42.545 -33.223 -22.936 -13.005 -3.327 +5.715 +13.792 C-C +32.588 +33.909 -56.210 -43.307 -29.566 -17.78 -7.722 +0.889 +8.509 +14.783 D-D +22.174 +21.031 -57.861 -40.792 -28.854 -17.221 -7.036 +0.406 +6.375 +10.871 E-E +7.518 -4.394 +55.855 -39.37 -25.578 -14.402 -5.867 +0.127 +3.835 +5.461 F-F -3.175 -8.280 -51.816 -34.214 -20.676 -10.795 -4.140 -0.330 +1.092 +0.457 G-G -8.89 +14.910 -48.743 -30.919 -17.170 -8.280 -3.073 -0.813 - 0.813 -2.819 Tenon -- +33.401 -41.199 -35.154 -29.083 -23.038 -16.967 -10.922 -4.851 +1.219 __________________________________________________________________________ SECTION 20 21 21A 22 23 __________________________________________________________________________ A-A +8.230 +10.668 +12.090 +13.132 -- B-B +8.992 +11.481 +12.7 +14.046 -- C-C +14.046 +18.440 +20.701 +22.809 -- D-D +19.685 +26.137 +20.413 +32.563 -- E-E +25.349 +33.833 +38.506 +42.316 -- F-F +29.388 +39.319 +44.628 +49.276 -- G-G +30.988 +39.319 +47.117 +52.07 -- Tenon +6.096 +7.874 -- +9.652 -- A-A +13.868 +22.276 +28.169 +34.087 +50.038 B-B +20.955 +27.381 +30.48 +33.604 -50.038 C-C +20.218 +25.222 +27.508 +29.769 -54.102 D-D +14.122 +16.51 +17.424 +18.313 -55.626 E-E +5.334 +3.658 -2.210 +0.787 -54.102 F-F -2.083 -6.452 -9.474 -12.497 -50.038 G-G -6.655 -12.192 -15.723 - 19.253 -46.99 Tenon +7.264 +13.335 -- +19.380 -- __________________________________________________________________________
The blade illustrated in FIGs. 1-5 was designed for a WEstinghouse BB73 turbine, for use in the L-1R row. The blade 30, having an airfoil portion 32, a root portion 34, and a platform portion 36, is wired to adjacent blades with a lashing wire 38. The tenon 40 is used to connect the blade 30 to adjacent blades through a shroud (not shown).
The blade depicted in FIGS. 1-5 has been commercially produced by the Westinghouse Electric Corporation and was designed the TS=1253A and 1254A. As shown in he drawings, these blades were lashed and shrouded and thus produced certain tuning effects as mentioned previously.
In redesigning the blade illustrated in FIGS. 1-5 for a retrofit, a need eixsted to eliminate traditional weak links such as lashign wires and tenons, to enhance the speed cycling capacity of the blade, to increase strength and to avoid aeroelastic instability. Moreover, the redesign should be effected using the same rotor grooves to minimize machining of the rotor.